20 lines
450 B
Text
20 lines
450 B
Text
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open eq is_trunc
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structure is_retraction [class] {A B : Type} (f : A → B) :=
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(sect : B → A)
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(right_inverse : Π(b : B), f (sect b) = b)
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definition foo
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{A : Type}
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{B : Type}
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(f : A → B)
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(g : B → A)
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(ε : Πb, f (g b) = b)
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(b b' : B)
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: is_retraction (λ (q : g b = g b'), (ε b) ⁻¹ ⬝ ap f q ⬝ ε b') :=
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begin
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fapply is_retraction.mk,
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{exact (@ap B A g b b') },
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{intro p, cases p, esimp {eq.ap, eq.rec_on, eq.idp} }
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end
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